Liouville Theorems Of Parabolic Differential Inequalities (and Systems) With Variable Coefficients In Cone

In this paper, we investigate the Liouville type theorems of parabolic differential inequalities and systems of coupling inequalities with variable coefficients in cone. First, we give the definition of global weak solution, and by constructing test function to establish the universal estimate which does not depend on the initial value of solution. The main feature of this method is that it does not use comparison theorems or the maximum principle.